Characterizing the magnetic noise power spectrum of dark spins in diamond
Coherence times of spin qubits in solid-state platforms are often limited by the presence of a spin bath. While some properties of these typically dark bath spins can be indirectly characterized via the central qubit, it is important to characterize their properties by direct measurement. Here we use pulsed electron paramagnetic resonance (pEPR) based Carr-Purcell-Meiboom-Gill (CPMG) dynamical decoupling to measure the magnetic noise power spectra for ensembles of P1 (substitutional nitrogen) centers in diamond that typically form the bath for NV (nitrogen-vacancy) centers. The experiments on the P1 centers were performed on a low [N] CVD (chemical vapor deposition) sample and a high [N] HPHT (high-temperature, high-pressure) sample at 89 mT. We characterize the NV centers of the latter sample using the same 2.5 GHz pEPR spectrometer. All power spectra show two distinct features, a broad component that is observed to scale as approximately $1/ω^{0.7-1.0}$, and a prominent peak at the $^{13}$C Larmor frequency. The behavior of the broad component is consistent with an inhomogeneous distribution of Lorentzian spectra due to clustering of P1 centers, which has recently been shown to be prevalent in HPHT diamond. It is unknown if such clustering occurs in CVD diamond. We develop techniques utilizing harmonics of the CPMG filter function to improve characterization of high-frequency signals, which we demonstrate on the $^{13}$C nuclear Larmor frequency. At 190 mT this is 2.04 MHz, 5.7 times higher than the CPMG modulation frequency ($<357$ kHz, hardware-limited). We assess the robustness of our methods in the presence of finite pulse widths and flip angle errors. Understanding the interactions of dark spins will inform methods of diamond fabrication for quantum technology. These techniques are applicable to ac magnetometry for nanoscale nuclear magnetic resonance and chemical sensing.